Slices, Not Selves: A Non-Inducibility Separation Framework for Global Coherence in Non-Abelian Constraint Systems

We present a structural separation framework for verification versus constructionbased on non-inducibility of global coherence in non-abelian constraint systems.Instances are formulated as group-valued edge-consistency (cocycle trivialization) problems on graphs,where a witness is a vertex labeling consistent with all edge constraints.Verification is local and polynomial-time.In contrast, we show that any ordered read-once process that constructs a global solution mustmaintain an internal state large enough to track a distributed non-abelian holonomy obstruction,yielding an explicit representational lower bound.We further embed an NP-hard label-cover family into a growing sequence of groups(e.g.\ $G_N=\SL_{n(N)}(\mathbb{F}_{q(N)})$), aligning hardness with distributed obstruction structure.The result is a rigorous non-inducibility mechanism for separating local slice verificationfrom global coherent induction within a precise computational model,with a synthesis theorem assembling the full chain.